Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition

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Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition)

Author : Min Ru
Publisher : World Scientific
ISBN 13 : 9811233527
Total Pages : 443 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) by : Min Ru

Download or read book Nevanlinna Theory And Its Relation To Diophantine Approximation (Second Edition) written by Min Ru and published by World Scientific. This book was released on 2021-03-10 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory.

Nevanlinna Theory and Its Relation to Diophantine Approximation

Author : Min Ru
Publisher :
ISBN 13 : 9789811233517
Total Pages : 426 pages
Book Rating : 4.2/5 (335 download)

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Book Synopsis Nevanlinna Theory and Its Relation to Diophantine Approximation by : Min Ru

Download or read book Nevanlinna Theory and Its Relation to Diophantine Approximation written by Min Ru and published by . This book was released on 2021 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved. Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory"--Provided by publisher.

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

Author : Junjiro Noguchi
Publisher : Springer Science & Business Media
ISBN 13 : 4431545719
Total Pages : 425 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by : Junjiro Noguchi

Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by Springer Science & Business Media. This book was released on 2013-12-09 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.

Nevanlinna Theory in Several Complex Variables and Diophantine Approximation

Author : Junjiro Noguchi
Publisher :
ISBN 13 : 9784431545729
Total Pages : 432 pages
Book Rating : 4.5/5 (457 download)

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Book Synopsis Nevanlinna Theory in Several Complex Variables and Diophantine Approximation by : Junjiro Noguchi

Download or read book Nevanlinna Theory in Several Complex Variables and Diophantine Approximation written by Junjiro Noguchi and published by . This book was released on 2013-12-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nevanlinna’s Theory of Value Distribution

Author : William Cherry
Publisher : Springer Science & Business Media
ISBN 13 : 9783540664161
Total Pages : 224 pages
Book Rating : 4.6/5 (641 download)

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Book Synopsis Nevanlinna’s Theory of Value Distribution by : William Cherry

Download or read book Nevanlinna’s Theory of Value Distribution written by William Cherry and published by Springer Science & Business Media. This book was released on 2001-04-24 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

Nevanlinna’s Theory of Value Distribution

Author : William Cherry
Publisher : Springer Science & Business Media
ISBN 13 : 3662125900
Total Pages : 214 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Nevanlinna’s Theory of Value Distribution by : William Cherry

Download or read book Nevanlinna’s Theory of Value Distribution written by William Cherry and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.

Arithmetic Geometry

Author : Jean-Louis Colliot-Thélène
Publisher : Springer
ISBN 13 : 3642159451
Total Pages : 251 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Arithmetic Geometry by : Jean-Louis Colliot-Thélène

Download or read book Arithmetic Geometry written by Jean-Louis Colliot-Thélène and published by Springer. This book was released on 2010-10-27 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

Introduction to Complex Hyperbolic Spaces

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475719450
Total Pages : 278 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Introduction to Complex Hyperbolic Spaces by : Serge Lang

Download or read book Introduction to Complex Hyperbolic Spaces written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the appearance of Kobayashi's book, there have been several re sults at the basic level of hyperbolic spaces, for instance Brody's theorem, and results of Green, Kiernan, Kobayashi, Noguchi, etc. which make it worthwhile to have a systematic exposition. Although of necessity I re produce some theorems from Kobayashi, I take a different direction, with different applications in mind, so the present book does not super sede Kobayashi's. My interest in these matters stems from their relations with diophan tine geometry. Indeed, if X is a projective variety over the complex numbers, then I conjecture that X is hyperbolic if and only if X has only a finite number of rational points in every finitely generated field over the rational numbers. There are also a number of subsidiary conjectures related to this one. These conjectures are qualitative. Vojta has made quantitative conjectures by relating the Second Main Theorem of Nevan linna theory to the theory of heights, and he has conjectured bounds on heights stemming from inequalities having to do with diophantine approximations and implying both classical and modern conjectures. Noguchi has looked at the function field case and made substantial progress, after the line started by Grauert and Grauert-Reckziegel and continued by a recent paper of Riebesehl. The book is divided into three main parts: the basic complex analytic theory, differential geometric aspects, and Nevanlinna theory. Several chapters of this book are logically independent of each other.

Minimal Surfaces through Nevanlinna Theory

Author : Min Ru
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110989557
Total Pages : 206 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Minimal Surfaces through Nevanlinna Theory by : Min Ru

Download or read book Minimal Surfaces through Nevanlinna Theory written by Min Ru and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-05-08 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Diophantine Approximations and Value Distribution Theory

Author : Paul Alan Vojta
Publisher : Springer
ISBN 13 : 3540474528
Total Pages : 141 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Diophantine Approximations and Value Distribution Theory by : Paul Alan Vojta

Download or read book Diophantine Approximations and Value Distribution Theory written by Paul Alan Vojta and published by Springer. This book was released on 2006-11-15 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Value Distribution Theory Related to Number Theory

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 3764375698
Total Pages : 546 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Value Distribution Theory Related to Number Theory by : Pei-Chu Hu

Download or read book Value Distribution Theory Related to Number Theory written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.

Heights in Diophantine Geometry

Author : Enrico Bombieri
Publisher : Cambridge University Press
ISBN 13 : 9780521712293
Total Pages : 676 pages
Book Rating : 4.7/5 (122 download)

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Book Synopsis Heights in Diophantine Geometry by : Enrico Bombieri

Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by Cambridge University Press. This book was released on 2006 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Number Theory

Author : W.A. Coppel
Publisher : Springer Science & Business Media
ISBN 13 : 9780387298511
Total Pages : 392 pages
Book Rating : 4.2/5 (985 download)

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Book Synopsis Number Theory by : W.A. Coppel

Download or read book Number Theory written by W.A. Coppel and published by Springer Science & Business Media. This book was released on 2006-02-02 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. Part A is accessible to first-year undergraduates and deals with elementary number theory. Part B is more advanced and gives the reader an idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches a broad picture is obtained. The book contains a treasury of proofs, several of which are gems seldom seen in number theory books.

Hyperbolic Complex Spaces

Author : Shoshichi Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 3662035820
Total Pages : 480 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Hyperbolic Complex Spaces by : Shoshichi Kobayashi

Download or read book Hyperbolic Complex Spaces written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.

Geometry and Analysis on Manifolds

Author : Takushiro Ochiai
Publisher : Springer
ISBN 13 : 3319115235
Total Pages : 481 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Geometry and Analysis on Manifolds by : Takushiro Ochiai

Download or read book Geometry and Analysis on Manifolds written by Takushiro Ochiai and published by Springer. This book was released on 2015-02-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.

Mathematics and Computation

Author : Avi Wigderson
Publisher : Princeton University Press
ISBN 13 : 0691189137
Total Pages : 434 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathematics and Computation by : Avi Wigderson

Download or read book Mathematics and Computation written by Avi Wigderson and published by Princeton University Press. This book was released on 2019-10-29 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

Distribution Theory of Algebraic Numbers

Author : Pei-Chu Hu
Publisher : Walter de Gruyter
ISBN 13 : 3110208261
Total Pages : 541 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Distribution Theory of Algebraic Numbers by : Pei-Chu Hu

Download or read book Distribution Theory of Algebraic Numbers written by Pei-Chu Hu and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions • Algebraic numbers • Algebraic geometry • Height functions • The abc-conjecture • Roth's theorem • Subspace theorems • Vojta's conjectures • L-functions.